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Delta Hedging in Financial Engineering: Towards a Model-Free Approach

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  • Michel Fliess

    () (ALIEN - Algebra for Digital Identification and Estimation - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - Ecole Centrale de Lille - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - CNRS - Centre National de la Recherche Scientifique - X - École polytechnique)

  • Cédric Join

    (ALIEN - Algebra for Digital Identification and Estimation - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - Ecole Centrale de Lille - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, CRAN - Centre de Recherche en Automatique de Nancy - UHP - Université Henri Poincaré - Nancy 1 - INPL - Institut National Polytechnique de Lorraine - CNRS - Centre National de la Recherche Scientifique)

Abstract

Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.

Suggested Citation

  • Michel Fliess & Cédric Join, 2010. "Delta Hedging in Financial Engineering: Towards a Model-Free Approach," Post-Print inria-00479824, HAL.
  • Handle: RePEc:hal:journl:inria-00479824
    Note: View the original document on HAL open archive server: https://hal.inria.fr/inria-00479824
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    References listed on IDEAS

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    1. Michel Fliess & C'edric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Papers 0901.1945, arXiv.org.
    2. Michel Fliess & Cédric Join & Mamadou Mboup, 2010. "Algebraic change-point detection," Post-Print inria-00439226, HAL.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Keywords

    Financial engineering; delta hedging; dynamic hedging; trends; quick fluctuations; abrupt changes; jumps; tracking control; model-free control;

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